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MultistepIntegrator (Commons Math 3.2 API)
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org.apache.commons.math3.ode</FONT>
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Class MultistepIntegrator</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><A HREF="../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">org.apache.commons.math3.ode.AbstractIntegrator</A>
      <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator</A>
          <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.ode.MultistepIntegrator</B>
</PRE>
<DL>
<DT><B>All Implemented Interfaces:</B> <DD><A HREF="../../../../../org/apache/commons/math3/ode/FirstOrderIntegrator.html" title="interface in org.apache.commons.math3.ode">FirstOrderIntegrator</A>, <A HREF="../../../../../org/apache/commons/math3/ode/ODEIntegrator.html" title="interface in org.apache.commons.math3.ode">ODEIntegrator</A></DD>
</DL>
<DL>
<DT><B>Direct Known Subclasses:</B> <DD><A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdamsIntegrator</A></DD>
</DL>
<HR>
<DL>
<DT><PRE>public abstract class <B>MultistepIntegrator</B><DT>extends <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdaptiveStepsizeIntegrator</A></DL>
</PRE>

<P>
This class is the base class for multistep integrators for Ordinary
 Differential Equations.
 <p>We define scaled derivatives s<sub>i</sub>(n) at step n as:
 <pre>
 s<sub>1</sub>(n) = h y'<sub>n</sub> for first derivative
 s<sub>2</sub>(n) = h<sup>2</sup>/2 y''<sub>n</sub> for second derivative
 s<sub>3</sub>(n) = h<sup>3</sup>/6 y'''<sub>n</sub> for third derivative
 ...
 s<sub>k</sub>(n) = h<sup>k</sup>/k! y<sup>(k)</sup><sub>n</sub> for k<sup>th</sup> derivative
 </pre></p>
 <p>Rather than storing several previous steps separately, this implementation uses
 the Nordsieck vector with higher degrees scaled derivatives all taken at the same
 step (y<sub>n</sub>, s<sub>1</sub>(n) and r<sub>n</sub>) where r<sub>n</sub> is defined as:
 <pre>
 r<sub>n</sub> = [ s<sub>2</sub>(n), s<sub>3</sub>(n) ... s<sub>k</sub>(n) ]<sup>T</sup>
 </pre>
 (we omit the k index in the notation for clarity)</p>
 <p>
 Multistep integrators with Nordsieck representation are highly sensitive to
 large step changes because when the step is multiplied by factor a, the
 k<sup>th</sup> component of the Nordsieck vector is multiplied by a<sup>k</sup>
 and the last components are the least accurate ones. The default max growth
 factor is therefore set to a quite low value: 2<sup>1/order</sup>.
 </p>
<P>

<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>2.0</DD>
<DT><B>Version:</B></DT>
  <DD>$Id: MultistepIntegrator.java 1463684 2013-04-02 19:04:13Z luc $</DD>
<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdamsBashforthIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><CODE>AdamsBashforthIntegrator</CODE></A>, 
<A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdamsMoultonIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><CODE>AdamsMoultonIntegrator</CODE></A></DL>
<HR>

<P>
<!-- ======== NESTED CLASS SUMMARY ======== -->

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<B>Nested Class Summary</B></FONT></TH>
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<CODE>static&nbsp;interface</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.NordsieckTransformer.html" title="interface in org.apache.commons.math3.ode">MultistepIntegrator.NordsieckTransformer</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Transformer used to convert the first step to Nordsieck representation.</TD>
</TR>
</TABLE>
&nbsp;<!-- =========== FIELD SUMMARY =========== -->

<A NAME="field_summary"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Field Summary</B></FONT></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear">Array2DRowRealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#nordsieck">nordsieck</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Nordsieck matrix of the higher scaled derivatives.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#scaled">scaled</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;First scaled derivative (h y').</TD>
</TR>
</TABLE>
&nbsp;<A NAME="fields_inherited_from_class_org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Fields inherited from class org.apache.commons.math3.ode.nonstiff.<A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdaptiveStepsizeIntegrator</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#mainSetDimension">mainSetDimension</A>, <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#scalAbsoluteTolerance">scalAbsoluteTolerance</A>, <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#scalRelativeTolerance">scalRelativeTolerance</A>, <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#vecAbsoluteTolerance">vecAbsoluteTolerance</A>, <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#vecRelativeTolerance">vecRelativeTolerance</A></CODE></TD>
</TR>
</TABLE>
&nbsp;<A NAME="fields_inherited_from_class_org.apache.commons.math3.ode.AbstractIntegrator"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Fields inherited from class org.apache.commons.math3.ode.<A HREF="../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">AbstractIntegrator</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#isLastStep">isLastStep</A>, <A HREF="../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#resetOccurred">resetOccurred</A>, <A HREF="../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#stepHandlers">stepHandlers</A>, <A HREF="../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#stepSize">stepSize</A>, <A HREF="../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#stepStart">stepStart</A></CODE></TD>
</TR>
</TABLE>
&nbsp;
<!-- ======== CONSTRUCTOR SUMMARY ======== -->

<A NAME="constructor_summary"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Constructor Summary</B></FONT></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected </CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#MultistepIntegrator(java.lang.String, int, int, double, double, double[], double[])">MultistepIntegrator</A></B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</A>&nbsp;name,
                    int&nbsp;nSteps,
                    int&nbsp;order,
                    double&nbsp;minStep,
                    double&nbsp;maxStep,
                    double[]&nbsp;vecAbsoluteTolerance,
                    double[]&nbsp;vecRelativeTolerance)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a multistep integrator with the given stepsize bounds.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected </CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#MultistepIntegrator(java.lang.String, int, int, double, double, double, double)">MultistepIntegrator</A></B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</A>&nbsp;name,
                    int&nbsp;nSteps,
                    int&nbsp;order,
                    double&nbsp;minStep,
                    double&nbsp;maxStep,
                    double&nbsp;scalAbsoluteTolerance,
                    double&nbsp;scalRelativeTolerance)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a multistep integrator with the given stepsize bounds.</TD>
</TR>
</TABLE>
&nbsp;
<!-- ========== METHOD SUMMARY =========== -->

<A NAME="method_summary"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Method Summary</B></FONT></TH>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#computeStepGrowShrinkFactor(double)">computeStepGrowShrinkFactor</A></B>(double&nbsp;error)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute step grow/shrink factor according to normalized error.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getMaxGrowth()">getMaxGrowth</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the maximal growth factor for stepsize control.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getMinReduction()">getMinReduction</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the minimal reduction factor for stepsize control.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getSafety()">getSafety</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the safety factor for stepsize control.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/ode/ODEIntegrator.html" title="interface in org.apache.commons.math3.ode">ODEIntegrator</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getStarterIntegrator()">getStarterIntegrator</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the starter integrator.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected abstract &nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear">Array2DRowRealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#initializeHighOrderDerivatives(double, double[], double[][], double[][])">initializeHighOrderDerivatives</A></B>(double&nbsp;h,
                               double[]&nbsp;t,
                               double[][]&nbsp;y,
                               double[][]&nbsp;yDot)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Initialize the high order scaled derivatives at step start.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#setMaxGrowth(double)">setMaxGrowth</A></B>(double&nbsp;maxGrowth)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Set the maximal growth factor for stepsize control.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#setMinReduction(double)">setMinReduction</A></B>(double&nbsp;minReduction)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Set the minimal reduction factor for stepsize control.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#setSafety(double)">setSafety</A></B>(double&nbsp;safety)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Set the safety factor for stepsize control.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#setStarterIntegrator(org.apache.commons.math3.ode.FirstOrderIntegrator)">setStarterIntegrator</A></B>(<A HREF="../../../../../org/apache/commons/math3/ode/FirstOrderIntegrator.html" title="interface in org.apache.commons.math3.ode">FirstOrderIntegrator</A>&nbsp;starterIntegrator)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Set the starter integrator.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#start(double, double[], double)">start</A></B>(double&nbsp;t0,
      double[]&nbsp;y0,
      double&nbsp;t)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Start the integration.</TD>
</TR>
</TABLE>
&nbsp;<A NAME="methods_inherited_from_class_org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Methods inherited from class org.apache.commons.math3.ode.nonstiff.<A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdaptiveStepsizeIntegrator</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#filterStep(double, boolean, boolean)">filterStep</A>, <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#getCurrentStepStart()">getCurrentStepStart</A>, <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#getMaxStep()">getMaxStep</A>, <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#getMinStep()">getMinStep</A>, <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#initializeStep(boolean, int, double[], double, double[], double[], double[], double[])">initializeStep</A>, <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#integrate(org.apache.commons.math3.ode.ExpandableStatefulODE, double)">integrate</A>, <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#resetInternalState()">resetInternalState</A>, <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#sanityChecks(org.apache.commons.math3.ode.ExpandableStatefulODE, double)">sanityChecks</A>, <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#setInitialStepSize(double)">setInitialStepSize</A>, <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#setStepSizeControl(double, double, double[], double[])">setStepSizeControl</A>, <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#setStepSizeControl(double, double, double, double)">setStepSizeControl</A></CODE></TD>
</TR>
</TABLE>
&nbsp;<A NAME="methods_inherited_from_class_org.apache.commons.math3.ode.AbstractIntegrator"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Methods inherited from class org.apache.commons.math3.ode.<A HREF="../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">AbstractIntegrator</A></B></TH>
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<A NAME="scaled"><!-- --></A><H3>
scaled</H3>
<PRE>
protected double[] <B>scaled</B></PRE>
<DL>
<DD>First scaled derivative (h y').
<P>
<DL>
</DL>
</DL>
<HR>

<A NAME="nordsieck"><!-- --></A><H3>
nordsieck</H3>
<PRE>
protected <A HREF="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear">Array2DRowRealMatrix</A> <B>nordsieck</B></PRE>
<DL>
<DD>Nordsieck matrix of the higher scaled derivatives.
 <p>(h<sup>2</sup>/2 y'', h<sup>3</sup>/6 y''' ..., h<sup>k</sup>/k! y<sup>(k)</sup>)</p>
<P>
<DL>
</DL>
</DL>

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<A NAME="MultistepIntegrator(java.lang.String, int, int, double, double, double, double)"><!-- --></A><H3>
MultistepIntegrator</H3>
<PRE>
protected <B>MultistepIntegrator</B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</A>&nbsp;name,
                              int&nbsp;nSteps,
                              int&nbsp;order,
                              double&nbsp;minStep,
                              double&nbsp;maxStep,
                              double&nbsp;scalAbsoluteTolerance,
                              double&nbsp;scalRelativeTolerance)
                       throws <A HREF="../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</A></PRE>
<DL>
<DD>Build a multistep integrator with the given stepsize bounds.
 <p>The default starter integrator is set to the <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/DormandPrince853Integrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><CODE>Dormand-Prince 8(5,3)</CODE></A> integrator with
 some defaults settings.</p>
 <p>
 The default max growth factor is set to a quite low value: 2<sup>1/order</sup>.
 </p>
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>name</CODE> - name of the method<DD><CODE>nSteps</CODE> - number of steps of the multistep method
 (excluding the one being computed)<DD><CODE>order</CODE> - order of the method<DD><CODE>minStep</CODE> - minimal step (must be positive even for backward
 integration), the last step can be smaller than this<DD><CODE>maxStep</CODE> - maximal step (must be positive even for backward
 integration)<DD><CODE>scalAbsoluteTolerance</CODE> - allowed absolute error<DD><CODE>scalRelativeTolerance</CODE> - allowed relative error
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</A></CODE> - if number of steps is smaller than 2</DL>
</DL>
<HR>

<A NAME="MultistepIntegrator(java.lang.String, int, int, double, double, double[], double[])"><!-- --></A><H3>
MultistepIntegrator</H3>
<PRE>
protected <B>MultistepIntegrator</B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</A>&nbsp;name,
                              int&nbsp;nSteps,
                              int&nbsp;order,
                              double&nbsp;minStep,
                              double&nbsp;maxStep,
                              double[]&nbsp;vecAbsoluteTolerance,
                              double[]&nbsp;vecRelativeTolerance)</PRE>
<DL>
<DD>Build a multistep integrator with the given stepsize bounds.
 <p>The default starter integrator is set to the <A HREF="../../../../../org/apache/commons/math3/ode/nonstiff/DormandPrince853Integrator.html" title="class in org.apache.commons.math3.ode.nonstiff"><CODE>Dormand-Prince 8(5,3)</CODE></A> integrator with
 some defaults settings.</p>
 <p>
 The default max growth factor is set to a quite low value: 2<sup>1/order</sup>.
 </p>
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>name</CODE> - name of the method<DD><CODE>nSteps</CODE> - number of steps of the multistep method
 (excluding the one being computed)<DD><CODE>order</CODE> - order of the method<DD><CODE>minStep</CODE> - minimal step (must be positive even for backward
 integration), the last step can be smaller than this<DD><CODE>maxStep</CODE> - maximal step (must be positive even for backward
 integration)<DD><CODE>vecAbsoluteTolerance</CODE> - allowed absolute error<DD><CODE>vecRelativeTolerance</CODE> - allowed relative error</DL>
</DL>

<!-- ============ METHOD DETAIL ========== -->

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<A NAME="getStarterIntegrator()"><!-- --></A><H3>
getStarterIntegrator</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/ode/ODEIntegrator.html" title="interface in org.apache.commons.math3.ode">ODEIntegrator</A> <B>getStarterIntegrator</B>()</PRE>
<DL>
<DD>Get the starter integrator.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>starter integrator</DL>
</DD>
</DL>
<HR>

<A NAME="setStarterIntegrator(org.apache.commons.math3.ode.FirstOrderIntegrator)"><!-- --></A><H3>
setStarterIntegrator</H3>
<PRE>
public void <B>setStarterIntegrator</B>(<A HREF="../../../../../org/apache/commons/math3/ode/FirstOrderIntegrator.html" title="interface in org.apache.commons.math3.ode">FirstOrderIntegrator</A>&nbsp;starterIntegrator)</PRE>
<DL>
<DD>Set the starter integrator.
 <p>The various step and event handlers for this starter integrator
 will be managed automatically by the multi-step integrator. Any
 user configuration for these elements will be cleared before use.</p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>starterIntegrator</CODE> - starter integrator</DL>
</DD>
</DL>
<HR>

<A NAME="start(double, double[], double)"><!-- --></A><H3>
start</H3>
<PRE>
protected void <B>start</B>(double&nbsp;t0,
                     double[]&nbsp;y0,
                     double&nbsp;t)
              throws <A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                     <A HREF="../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</A>,
                     <A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A>,
                     <A HREF="../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</A></PRE>
<DL>
<DD>Start the integration.
 <p>This method computes one step using the underlying starter integrator,
 and initializes the Nordsieck vector at step start. The starter integrator
 purpose is only to establish initial conditions, it does not really change
 time by itself. The top level multistep integrator remains in charge of
 handling time propagation and events handling as it will starts its own
 computation right from the beginning. In a sense, the starter integrator
 can be seen as a dummy one and so it will never trigger any user event nor
 call any user step handler.</p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>t0</CODE> - initial time<DD><CODE>y0</CODE> - initial value of the state vector at t0<DD><CODE>t</CODE> - target time for the integration
 (can be set to a value smaller than <code>t0</code> for backward integration)
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if arrays dimension do not match equations settings
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</A></CODE> - if integration step is too small
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - if the number of functions evaluations is exceeded
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</A></CODE> - if the location of an event cannot be bracketed</DL>
</DD>
</DL>
<HR>

<A NAME="initializeHighOrderDerivatives(double, double[], double[][], double[][])"><!-- --></A><H3>
initializeHighOrderDerivatives</H3>
<PRE>
protected abstract <A HREF="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear">Array2DRowRealMatrix</A> <B>initializeHighOrderDerivatives</B>(double&nbsp;h,
                                                                       double[]&nbsp;t,
                                                                       double[][]&nbsp;y,
                                                                       double[][]&nbsp;yDot)</PRE>
<DL>
<DD>Initialize the high order scaled derivatives at step start.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>h</CODE> - step size to use for scaling<DD><CODE>t</CODE> - first steps times<DD><CODE>y</CODE> - first steps states<DD><CODE>yDot</CODE> - first steps derivatives
<DT><B>Returns:</B><DD>Nordieck vector at first step (h<sup>2</sup>/2 y''<sub>n</sub>,
 h<sup>3</sup>/6 y'''<sub>n</sub> ... h<sup>k</sup>/k! y<sup>(k)</sup><sub>n</sub>)</DL>
</DD>
</DL>
<HR>

<A NAME="getMinReduction()"><!-- --></A><H3>
getMinReduction</H3>
<PRE>
public double <B>getMinReduction</B>()</PRE>
<DL>
<DD>Get the minimal reduction factor for stepsize control.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>minimal reduction factor</DL>
</DD>
</DL>
<HR>

<A NAME="setMinReduction(double)"><!-- --></A><H3>
setMinReduction</H3>
<PRE>
public void <B>setMinReduction</B>(double&nbsp;minReduction)</PRE>
<DL>
<DD>Set the minimal reduction factor for stepsize control.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>minReduction</CODE> - minimal reduction factor</DL>
</DD>
</DL>
<HR>

<A NAME="getMaxGrowth()"><!-- --></A><H3>
getMaxGrowth</H3>
<PRE>
public double <B>getMaxGrowth</B>()</PRE>
<DL>
<DD>Get the maximal growth factor for stepsize control.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>maximal growth factor</DL>
</DD>
</DL>
<HR>

<A NAME="setMaxGrowth(double)"><!-- --></A><H3>
setMaxGrowth</H3>
<PRE>
public void <B>setMaxGrowth</B>(double&nbsp;maxGrowth)</PRE>
<DL>
<DD>Set the maximal growth factor for stepsize control.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>maxGrowth</CODE> - maximal growth factor</DL>
</DD>
</DL>
<HR>

<A NAME="getSafety()"><!-- --></A><H3>
getSafety</H3>
<PRE>
public double <B>getSafety</B>()</PRE>
<DL>
<DD>Get the safety factor for stepsize control.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>safety factor</DL>
</DD>
</DL>
<HR>

<A NAME="setSafety(double)"><!-- --></A><H3>
setSafety</H3>
<PRE>
public void <B>setSafety</B>(double&nbsp;safety)</PRE>
<DL>
<DD>Set the safety factor for stepsize control.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>safety</CODE> - safety factor</DL>
</DD>
</DL>
<HR>

<A NAME="computeStepGrowShrinkFactor(double)"><!-- --></A><H3>
computeStepGrowShrinkFactor</H3>
<PRE>
protected double <B>computeStepGrowShrinkFactor</B>(double&nbsp;error)</PRE>
<DL>
<DD>Compute step grow/shrink factor according to normalized error.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>error</CODE> - normalized error of the current step
<DT><B>Returns:</B><DD>grow/shrink factor for next step</DL>
</DD>
</DL>
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